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http://dx.doi.org/10.4134/BKMS.2012.49.5.1089

SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ  

Pyo, Jun-Cheol (Department of Mathematics Pusan National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1089-1099 More about this Journal
Abstract
We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.
Keywords
complete minimal surface; singly-periodic surface; product space;
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